Minimising the communication latency and achieving considerable scalability are of paramount importance when designing high performance broadcast algorithms. Many algorithms for wormhole-switched meshes have been widely reported in the literature. However, most of these algorithms handle broadcast in a sequential manner and do not scale well with the network size. As a consequence, many parallel applications cannot be efficiently supported using existing algorithms. Motivated by these observations, this paper presents a new broadcast algorithm for the all-port mesh networks. The unique feature of the proposed algorithm is its capability of handling broadcast in only one message-passing step irrespective of the network size. Results from a comparative analysis and simulation reveal that the proposed algorithm exhibits superior performance characteristics over those of the well-known Recursive Doubling, Extending Dominating Node and Network Partitioning algorithms.